The uniform-time prior, on the other hand, is representative of local measures, which focus on a space-time region around a time-like observer [1]}, [2]}, [3]}, [4]}, [5]}.
Because a typical world-line ends in a terminal vacuum well-before the mixing time for the landscape, the resulting probabilities differ markedly from the quasi-stationary distribution. Relatedly, an alternative framework developed recently [6]}, [7]}, [8]}, [9]}, [10]} suggests that we live during the approach to equilibrium. (See [11]} for related ideas.)
The resulting early-time measure [9]} favors vacua that can be accessed early on in the evolution, instead of vacua that are frequently generated in the asymptotic future. We will show in Sec. REF  that the probabilities with uniform-time prior coincide with Bousso's prior probabilities [1]}As explained in Sec. REF , Bousso first considers the ensemble of possible future “histories" of a world-line. The probability of different histories coincides with our uniform-time predictive probabilities. Bousso then considers the causal diamond of each world-line in the ensemble, and calculates the fraction of observers making different observations within this causal diamond. Because we are interested in prior predictive probabilities, without any anthropic conditioning, this second aspect in Bousso's construction is not relevant for our purposes., and are closely related to Garriga and Vilenkin's “comoving" probabilities [14]}, [15]}. We refer to this case as the uniform-time hypothesis \({\cal H}_{\rm uni}\) .
